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Introduction to Mathematical Statistics 8th Edition



Introduction to Mathematical Statistics 8th Edition PDF

Author: Robert Hogg, Joseph McKean

Publisher: Pearson

Genres:

Publish Date: January 10, 2018

ISBN-10: 0134686993

Pages: 768

File Type: PDF

Language: English

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Book Preface

We have made substantial changes in this edition of Introduction to Mathematical Statistics. Some of these changes help students appreciate the connection between statistical theory and statistical practice while other changes enhance the develop-ment and discussion of the statistical theory presented in this book.
Many of the changes in this edition reflect comments made by our readers. One of these comments concerned the small number of real data sets in the previous editions. In this edition, we have included more real data sets, using them to illustrate statistical methods or to compare methods. Further, we have made these data sets accessible to students by including them in the free R package hmcpkg. They can also be individually downloaded in an R session at the url listed below. In general, the R code for the analyses on these data sets is given in the text.
We have also expanded the use of the statistical software R. We selected R because it is a powerful statistical language that is free and runs on all three main platforms (Windows, Mac, and Linux). Instructors, though, can select another statistical package. We have also expanded our use of R functions to compute analyses and simulation studies, including several games. We have kept the level of coding for these functions straightforward. Our goal is to show students that with a few simple lines of code they can perform significant computations. Appendix B contains a brief R primer, which suffices for the understanding of the R used in the text. As with the data sets, these R functions can be sourced individually at the cited url; however, they are also included in the package hmcpkg.
We have supplemented the mathematical review material in Appendix A, placing it in the document Mathematical Primer for Introduction to Mathematical Statistics. It is freely available for students to download at the listed url. Besides sequences, this supplement reviews the topics of infinite series, differentiation, and integra-tion (univariate and bivariate). We have also expanded the discussion of iterated integrals in the text. We have added figures to clarify discussion.
We have retained the order of elementary statistical inferences (Chapter 4) and asymptotic theory (Chapter 5). In Chapters 5 and 6, we have written brief reviews of the material in Chapter 4, so that Chapters 4 and 5 are essentially independent of one another and, hence, can be interchanged. In Chapter 3, we now begin the section on the multivariate normal distribution with a subsection on the bivariate normal distribution. Several important topics have been added. This includes Tukey’s multiple comparison procedure in Chapter 9 and confidence intervals for the correlation coefficients found in Chapters 9 and 10. Chapter 7 now contains a discussion on standard errors for estimates obtained by bootstrapping the sample. Several topics that were discussed in the Exercises are now discussed in the text. Examples include quantiles, Section 1.7.1, and hazard functions, Section 3.3. In general, we have made more use of subsections to break up some of the discussion. Also, several more sections are now indicated by ∗ as being optional.
Content and Course Planning
Chapters 1 and 2 develop probability models for univariate and multivariate vari-ables while Chapter 3 discusses many of the most widely used probability models. Chapter 4 discusses statistical theory for much of the inference found in a stan-dard statistical methods course. Chapter 5 presents asymptotic theory, concluding with the Central Limit Theorem. Chapter 6 provides a complete inference (esti-mation and testing) based on maximum likelihood theory. The EM algorithm is also discussed. Chapters 7–8 contain optimal estimation procedures and tests of statistical hypotheses. The final three chapters provide theory for three important topics in statistics. Chapter 9 contains inference for normal theory methods for basic analysis of variance, univariate regression, and correlation models. Chapter 10 presents nonparametric methods (estimation and testing) for location and uni-variate regression models. It also includes discussion on the robust concepts of efficiency, influence, and breakdown. Chapter 11 offers an introduction to Bayesian methods. This includes traditional Bayesian procedures as well as Markov Chain Monte Carlo techniques.
Several courses can be designed using our book. The basic two-semester course in mathematical statistics covers most of the material in Chapters 1–8 with topics selected from the remaining chapters. For such a course, the instructor would have the option of interchanging the order of Chapters 4 and 5, thus beginning the second semester with an introduction to statistical theory (Chapter 4). A one-semester course could consist of Chapters 1–4 with a selection of topics from Chapter 5. Under this option, the student sees much of the statistical theory for the methods discussed in a non-theoretical course in methods. On the other hand, as with the two-semester sequence, after covering Chapters 1–3, the instructor can elect to cover Chapter 5 and finish the course with a selection of topics from Chapter 4.


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